The metric dimension of k-subdivision graphs

L. Susilowati; S. Zahidah; R. D. Nastiti; M. I. Utoyo

doi:10.1088/1742-6596/1494/1/012015

The metric dimension of k-subdivision graphs

L. Susilowati, S. Zahidah, R. D. Nastiti, M. I. Utoyo

Research output: Contribution to journal › Conference article › peer-review

3 Citations (Scopus)

Abstract

The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k-subdivision denoted by S_k (G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs S_k (G), specifically for some special graphs, those are path graph (P_n), cycle graph (C_n), complete graph (K_n), star graph (S_n), ladder graph (L_n), book graph (B_n), wheel graph (W_n) and fan graph (F_n).

Original language	English
Article number	012015
Journal	Journal of Physics: Conference Series
Volume	1494
Issue number	1
DOIs	https://doi.org/10.1088/1742-6596/1494/1/012015
Publication status	Published - 27 May 2020
Event	Soedirman''s International Conference on Mathematics and Applied Sciences 2019, SICoMAS 2019 - Purwokerto, Indonesia Duration: 23 Oct 2019 → 24 Oct 2019

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title = "The metric dimension of k-subdivision graphs",

abstract = "The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k-subdivision denoted by Sk (G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs Sk (G), specifically for some special graphs, those are path graph (Pn), cycle graph (Cn), complete graph (Kn), star graph (Sn), ladder graph (Ln), book graph (Bn), wheel graph (Wn) and fan graph (Fn).",

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AU - Zahidah, S.

AU - Nastiti, R. D.

AU - Utoyo, M. I.

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PY - 2020/5/27

Y1 - 2020/5/27

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AB - The concept of metric dimension of graph could be applied in many graphs, one of them is subdivision graph. A subdivision graph of graph G denoted as S(G) is a graph resulting from graph G by replacing an edge uv with a new vertex w and adding two new edges uw and wv. In this paper, the subdivision graph is called k-subdivision denoted by Sk (G), if the number of edges replaced from graph G is k for 1 ≤ k ≤ |E(G)|, where |E(G)| is the size of graph G. The purpose of this research is to find the metric dimension of subdivision graphs Sk (G), specifically for some special graphs, those are path graph (Pn), cycle graph (Cn), complete graph (Kn), star graph (Sn), ladder graph (Ln), book graph (Bn), wheel graph (Wn) and fan graph (Fn).

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The metric dimension of k-subdivision graphs

Abstract

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